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Model predictive control (MPC) is widely used for path tracking of autonomous vehicles due to its ability to handle various types of constraints. However, a considerable predictive error exists because of the error of mathematics model or the model linearization. In this paper, we propose a framework combining the MPC with a learning-based error estimator and a feedforward compensator to improve the path tracking accuracy. An extreme learning machine is implemented to estimate the model based predictive error from vehicle state feedback information. Offline training data is collected from a vehicle controlled by a model-defective regular MPC for path tracking in several working conditions, respectively. The data include vehicle state and the spatial error between the current actual position and the corresponding predictive position. According to the estimated predictive error, we then design a PID-based feedforward compensator. Simulation results via Carsim show the estimation accuracy of the predictive error and the effectiveness of the proposed framework for path tracking of an autonomous vehicle.